Question

The sum of the first 'n' even natural numbers is

• A. $2n^2$
• B. $n(n+1)$
• C. $n(n+1{)}^2$
• D. $n(n+1{)}^3$

Answer 1

The correct option is B $n(n+1)$

Sum of first 'n' even natural numbers $=2+4+6+8....+2n=2(1+2+3+4...+n)$
But since sum of first 'n' natural numbers $=\frac{n(n+1)}{2}$
So, Sum of first 'n' even natural numbers $=2+4+6+8....+2n=2(1+2+3+\mathrm{4...}+n)=2\times \frac{n(n+1)}{2}=n(n+1)$